
auflegen
to hang up
To end a phone call by placing the receiver back on the cradle or pressing the corresponding button.
Er wurde wütend und hat einfach aufgelegt.
He got angry and simply hung up.
to hang up / put on / launch
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to hang up
To end a phone call by placing the receiver back on the cradle or pressing the corresponding button.
Er wurde wütend und hat einfach aufgelegt.
He got angry and simply hung up.

to put on
To put something onto a surface, often carefully or for a specific purpose.
Der Kellner legte die saubere Tischdecke auf.
The waiter put on the clean tablecloth.

to DJ
To play music as a DJ in a club, at a party, or on the radio.
Welcher DJ legt heute Abend im Club auf?
Which DJ is DJing at the club tonight?

to launch
To start or publish a program, a fund, or a new edition of a book.
Die Regierung hat ein neues Förderprogramm für Start-ups aufgelegt.
The government has launched a new funding program for start-ups.

to apply
To apply makeup, powder, or lipstick to the face.
Vor dem Ausgehen legt sie immer etwas Lippenstift auf.
Before going out, she always applies a little lipstick.
'Auflegen' is a separable verb. The prefix 'auf' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der DJ legt gleich seine besten Platten auf.
The DJ is about to put on his best records.
The meaning of 'auflegen' depends strongly on the object. The context makes clear whether you are ending a phone call, working as a DJ, launching a program, or putting something onto a surface.
Er legte wütend auf.
He hung up angrily.
In the meaning 'ein Telefongespräch beenden' (to end a phone call), 'auflegen' is often used without an object when it is clear from context that it is about a phone call.
Sprich lauter, leg noch nicht auf!
Speak louder, don't hang up yet!
When someone 'auflegt' (DJs), in the context of parties or clubs, it means that this person is playing music as a DJ. This meaning is rather colloquial.
Am Freitag legt eine bekannte DJane aus Berlin auf.
On Friday, a well-known female DJ from Berlin is DJing.
In a more formal, often economic or political context, 'auflegen' means to initiate something. Typical objects are 'ein Programm' (a program), 'einen Fonds' (a fund), or 'eine Anleihe' (a bond).
Die Bank hat einen neuen Fonds für nachhaltige Investitionen aufgelegt.
The bank has launched a new fund for sustainable investments.
In connection with cosmetics, 'auflegen' means the same as 'auftragen' (to apply). It is often used for powder, blush, or lipstick.
Sie legte vor dem Spiegel noch schnell etwas Puder auf.
She quickly applied a little powder in front of the mirror.
to play
Both words can refer to playing music in a club or at a party. „Spielen“ generally says that music is being played or performed. „Auflegen“ is more specific and refers to a DJ’s activity of selecting and playing music for the audience. „Auflegen“ is therefore especially suitable for the activity of a DJ.

Der DJ legt heute Abend Musik in demselben kleinen Club auf.
The DJ is playing music at the same small club this evening.
Die Band spielt heute Abend Musik in einem kleinen Club.
The band is playing music at a small club this evening.